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an author's http://oatao.univ-toulouse.fr/22987
https://doi.org/10.1016/j.compositesa.2018.01.018
Labanieh, Ahmad Rashed and Garnier, Christian and Ouagne, Pierre
and Dalverny, Olivier and Soulat, Damien Intra-
ply yarn sliding defect in hemisphere preforming of a woven
preform. (2018) Composites Part A: Applied Science
and Manufacturing, 107. 432-446. ISSN 1359835X
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Intra-ply yarn sliding defect in hemisphere preforming of a
woven preform
Ahmad Rashed Labanieha,⁎, Christian Garnierb, Pierre Ouagneb,
Olivier Dalvernyb,Damien Soulata
aUniversity of Lille, GEMTEX, ENSAIT, 2 allée Louise et Victor
Champier, 59056 Roubaix, Franceb LGP, ENIT, 47 avenue d'Azereix,
65016 Tarbes, France
Keywords:A. Fabrics/textilesB. DefectsB. Internal frictionE.
Preforming
A B S T R A C T
Preforming is the first step to manufacture a complex composite
part via Liquid Composite Moulding processes.The defects that may
be encountered during this phase within the preform architecture
may decrease the ex-pected mechanical performances of the final
part. The intra-ply yarn sliding is a defect frequently
observedduring preforming of a woven preform but its mechanism is
far from being fully understood. The aim of thisstudy is to analyse
the mechanism of this defect arising when preforming of a carbon
woven fabric into hemi-spheric shape. An experimental study
followed by analytical analysis was performed to evaluate the
effect of theprocess parameters, material properties and ply
configuration conditions on the yarn tension and contactstresses. A
significant effect of the yarn tension and the contact shear
stresses on the defect occurrence wasdemonstrated. Based on this
analysis, solutions were tested with success to prevent this
defect.
1. Introduction
To manufacture complex composite parts, Liquid CompositeMoulding
(LCM) processes [1] offer a good compromise in terms
ofrepeatability, production rates, low-energy consumption and low
finalcost [2]. The first step of these processes consists in
draping a drypreform before the liquid resin is injected.
Preforming is a difficultphase, and the physical mechanisms are
complex because they dependon many parameters (shape of tools,
characteristics of the preform,number and orientation of plies,
loads applied, etc.). If the mechanicalloadings (tension, shear,
compression, bending, friction, etc.) to whichthe reinforcements
are subjected during the preforming step have beenwell described in
the literature [3–6], the generation and the control ofdefects are
far from being entirely understood. At the macroscopic
scale(preform scale) wrinkling is one of the defects that occurs
most often.Boisse et al. [7] recently explained that the frequency
of occurrence ofthe wrinkling defect was related to the weak
textile bending stiffnessdue to possible slippage between fibres.
Several numerical [8–10] andexperimental [11–13] studies focused on
the influence of blank holdersor other systems to prevent wrinkles.
These tools confer global tensiledeformations at their vicinity and
it was demonstrated that inducedtensile forces in the fibre
direction prevent wrinkling [14]. In the caseof preforming tests on
complex shapes of multilayer, which are thesubjects of recent
papers [2,14–16], Nezami et al. [17] underlined that,friction-based
blank holders or other systems may reduce wrinkling, but
induce other defects in the fabric, such as parallel fibre
distortionswithout gaps, fibre distortions with small/large gaps,
filament damage,broken or pulled out roving. Except for filament
damage, these defectsoccur at the mesoscopic scale (tows, yarn).
This is also the case of towbuckles. This defect is described in
[17–20]. It can be reduced by thecontrol of tensile deformation as
shown in [21]. Another type of de-fects, less studied in the
literature, can be defined as intra-ply slippagewhich occurs
between the warp and the weft yarns of a woven re-inforcement. In
this case, the tow or yarn orientation cannot be con-trolled during
the preforming step and the local pore spaces are thusmodified.
Large empty spaces can be observed between the yarn. Lo-cally, the
density of fibre may be reduced to very low values. As
aconsequence, the local permeability components for the injection
steps[22], [23] are drastically modified, and one can expect to
obtain resinrich zones within the composite part. This surely means
that zones ofweakness for the composite part are created. Allaoui
et al. [13] haveexperimentally shown large yarn slippage on the
vertical faces of a glassplain weave prismatic preform. Boisse et
al. [7] described the numericalcomplexity to model this loss of
cohesion of the woven network [24],and the need to use mesoscopic
finite element models to allow thepossible slippage between yarns.
This slippage mechanism was alsodescribed during the bias-extension
test [3,25], especially for largeshear angles. During this test
where the analytical kinematic [26,27]can predict theoretically the
shear angle, the differences observed withmeasured angles can be
explained by this slippage between yarns as the
⁎ Corresponding author.E-mail addresses:
[email protected] (A.R. Labanieh), [email protected]
(C. Garnier), [email protected] (P. Ouagne),
[email protected] (O. Dalverny),
[email protected] (D. Soulat).
T
https://doi.org/10.1016/j.compositesa.2018.01.018mailto:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]://doi.org/10.1016/j.compositesa.2018.01.018http://crossmark.crossref.org/dialog/?doi=10.1016/j.compositesa.2018.01.018&domain=pdf
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pressures 0.025 and 0.075MPa that correspond to normal forces
byeach cylinder equals to 77.9 and 233.7 N respectively, according
to theactuator specifications. These operating pressures were
chosen after afirst preliminary set of test and are related to the
appearance of theintra-ply yarn sliding defect. When the minimum
operating pressure(0.025MPa) is applied, no sliding defect occurs.
From an applied op-erating pressure of 0.075MPa this defect takes
place. The upper plate isconsidered as the blank-holder because it
is the mobile plate and thenormal force (P) is applied on its top
surface, Fig. 1. The force (P) iscalled the holder force all over
this paper. The lower plate is consideredas the die since it is
fixed into position in this machine configuration.For each
experiment, the preforming force exerted by the punch is re-corded
as a function of the punch displacement. The force measurementis
performed by means of a load cell mounted between the punch andthe
driving actuator. Also, the ply draw-in, border position and
yarnarrangement after preforming are captured by a CCD camera.
Thecamera is placed on the top side and its optical axis is aligned
with thepunch movement path.
2.2. Material properties and ply geometry
The commercial fabric “Hexcel HexForce 48,600 U 1250” was usedin
this study to perform the experimental work. It is classified as a
2Dwoven fabric made with a twill 2/2 weaving architecture and
con-structed of 3.7 warps/cm and 3.7 wefts/cm with a nominal area
densityof 600 g/m2 and a nominal thickness of 0.62mm. The
constituentyarns, both warp and weft, are “AS4 C GP 12 K” high
strength carbonfibres and they have a linear density of 0.8 g/m.
Both yarns are nottwisted and not powdered.
The forming tests were conducted using one ply of the woven
fabriccut in a square shape with 260mm side length. The fabric
specimenswere visually inspected and specifically chosen so that
they are free ofdefect at the beginning of the forming test. The
tests were performedusing two initial orientations (0° and 45°) of
the fabric on the die aspresented in Fig. 2. The dashed lines
sketched on the ply in Fig. 2 re-present the warp and weft yarns
passing through the punch main axisand aligned with the radius of
the hole. These yarns are called radialyarn in the next sections.
On the 0° orientation ply, the warp and weftyarns are parallel to
the plate side edges, Fig. 2-a. For the 45° or-ientation, the warp
and weft yarns are parallel to the plate diagonal and
Fig. 1. Forming machine scheme with characteristicdimensions.
All dimensions are in mm.
theoretical kinematic is based on non-slippage mechanisms. This
slip-page phenomenon is localised at the intersection of the three
zones classically defined in this in-plane shear test. Concerning
the in-plane shear behaviour identified by the bias-extension test
of an unbalanced woven fabric, Barbagello et al. [28] noted the
presence of measurable yarn slippages (up to a maximum that is
around 10% of the total length of the yarns). In papers dedicated
to the preforming of NCF fabrics [29–30] intra-ply slippage between
fibres has been observed, without solutions to prevent or reduce
this defect qualified as irreversible in [30]. Except in these
studies, few articles of the literature deal with this type of
defect. In this paper, experimental preforming tests were
con-ducted on a carbon twill weave fabric. The slippage phenomenon
oc-curred in zones with low shear angles, for specific ply
orientation. Yarn tensions were analytically computed relatively to
tools load to under-stand this slippage defect. The influence of
the ply orientation and the ply dimension were experimentally
studied to reduce tension in yarns and reduce this slippage.
Finally, solutions based on the geometry of tools were proposed to
prevent this type of defect.
2. Experimental conditions
2.1. Forming machine
Fig. 1 shows the experimental preforming machine developed at
the GEMTEX laboratory [16,31]. The machine is composed of three
basic parts: a punch and two square-shaped plates. In this study, a
punch with hemisphere geometry (double curved surface) of a
diameter of 100 mm was used. The punch movement is controlled by a
pneumatic actuator with a constant mounting speed (45 mm/s).
Both upper and lower plates are a square shaped plate of 300 mm
side length. The upper plate is made of Plexiglas and it has a
thickness of 20 mm. Both plates have a circular hole in its centre.
The hole dia-meter of the upper plate is 110.8 mm and its corner
edge is machined from the fabric side. The lower plate is fixed
into position whereas the upper one is mobile, parallel to the
punch axis. This allows the ar-rangement of the fabric ply between
the two plates in the desired or-ientation. The upper plate is
subjected to a normal pressure applied by four pneumatic actuators
placed on the plate corners. This normal pressure is controlled by
the pressure of the compressed air supplied to the actuators. The
experiments were conducted with two operating
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they create an angle of 45° with plate side edge, Fig. 2-b. The
plies with0° and 45° orientations are denoted across this paper as
ply-0 and ply-45respectively. One can note that the length of the
portion of the radialyarns which is in contact with the two upper
and lower plates is dif-ferent for both orientations. In ply-0, a
half of this length is marked asL0=68.6 mm whereas in ply-45 it is
marked as L45= 122.5mm asillustrated in Fig. 2.
3. Definition of the intra-ply yarn sliding defect
Intra-ply yarn sliding occurs relatively frequently when
preforminga woven reinforcement. This textile preform is
constructed by interla-cing two orthogonal sets of yarn. As a
result of this interlacement, aninter-yarn friction force is
induced at the over crossing area between thetwo yarn sets. This
force ensures the cohesion of the fabric network andit is
responsible of the effort transmission between the yarns. It
dependson the fabric architecture, yarn material and structure and
yarn tension.
The Fig. 3 shows a representative scheme of this defect on a
wovenpreform. When the longitudinal yarns are translated along
their mainaxis (as they are driven by the punch during preforming),
they bring thetransversal yarns with them by means of the
inter-yarn friction force.However, when the applied efforts on a
transversal yarn, such as axialtension or tangential friction force
on the yarn exposed surface, over-comes the inter-yarn friction
force, the transversal yarn is locked intoposition and the
longitudinal yarns slide across it. Thus, a gap occursbetween the
locked transversal yarns and the last transversal yarnbrought with
the longitudinal ones. This created defect zone on thepreform is
characterised on Fig. 3 as a zone with a low density of
thetransversal yarns. In the right-below-the-gap zone, the locked
yarnsaccumulate creating a higher density zone. This accumulation
of theyarns causes an important increase of the contact pressure
and theinter-yarn friction force on the crossing area between the
two yarn sets.That enhances the cohesion of the fabric network and
stops the yarnsslippage. Hence, this defect is a local
disarrangement of the transversal
Fig. 2. Dimensions and placement of the plies on the machine
under the blank holder plate, ply-0 (a) ply-45 (b). Dashed lines
represent the radial warp and weft yarns. All dimensions arein
mm.
Fig. 3. Representative scheme for the intra-ply yarnsliding
defect on a plain woven ply.
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yarn alignment.Hence, the intra-ply yarn sliding defect could be
defined as a loss of
cohesion between the two orthogonal yarn sets constructing the
wovenply [24]. It occurs in the ply plane (no out-of-plane
deformation) and itis characterised by a low density zone (with a
gap) followed by a higherdensity zone, Fig. 3. The amplitude of
this defect can be expressed bythe gap length and width and number
of the involved yarns. It is im-portant to note that the amplitude
of the sliding defect may be large andsome transversal yarns on the
ply borders may get out of the fabricnetwork, as presented in
[24].
4. Results
4.1. Preforming force
Fig. 4 shows the preforming force as a function of the punch
dis-placement for both ply-0 and ply-45 when preforming with the
twooperating pressures for the holder actuators. The experiments
wererepeated three times at the pressure (0.025 and 0.075MPa) for
both plyorientations. The mean value of the recorded force is
presented on thegraph with error bars pointing out the standard
deviation of the mea-surements. It is clear from Fig. 4 that the
augmentation of the blankholder force causes the increase of the
preforming force for both plyorientations. This is the results of a
higher friction force standingagainst the ply sliding across the
die and blank holder surfaces. Thepreforming of a ply with an
initial 45° orientation requires higher effortin comparison to
ply-0 in spite of similar blank holder pressure andidentical
initial ply dimension and shape as shown in Fig. 2. The
forcerelative differences are about 56% and 63% for ply-0 at
maximumdisplacement of the punch for the operating pressure of
0.025MPa and0.075MPa respectively.
4.2. Intra-ply yarn sliding defect
Intra-ply yarn sliding defect was observed when preforming
ply-45with 0.075MPa operating pressure on the three tested
samples.However, it was not remarked with lower pressure (0.025MPa)
nor forply-0 with both applied operating pressures. The intra-ply
yarn slidingoccurred in the non-sheared zone of the ply on the
rounded corner ofthe upper plate hole, Fig. 5-a.
In order to characterise this defect, the yarns position after
pre-forming and the local relative inter-yarn slippage have to be
spotted.
However, the carbon fibres are characterised by a light
reflecting sur-face. Furthermore, the normal orientation and
altitude of the useful part(3D deformed) of the ply surface change
during the preforming process.Therefore white dots have been
speckled on the apparent yarn surfacewith an alternative pattern
(one with a dot and one with no dot).Namely, for a unit cell of the
fabric composed of four warp and fourweft yarns, 9 dots are
speckled; 4 on corners, 4 on mid-points of sidesegments and 1 in
the centre, Fig. 5-b. The dots have been speckled overa diagonal
portion of the ply, as shown in Fig. 5-a, where the defect
isexpected to take place. To distinguish between longitudinal
andtransversal yarns over this diagonal part, round (red) and cross
(blue)marks were superimposed to the white dots on the treated
photos.
On the zoomed rectangle zone ABCD defined in Fig. 5-a, the
yarnslippage defect is expected to take place. The yarns
arrangements wereobserved before and after preforming. Before
preforming, that corre-sponds to the initial planar state of the
ply (Fig. 5-b), the yarn count perunit length is uniform (same
distance between dots). Furthermore, thedots belonging to the
transversal yarn are aligned with the corre-sponding longitudinal
yarns. The path of the longitudinal yarns wasdetermined by spline
connecting the dots. Similarly, the dots belongingto the
longitudinal yarns are also aligned with corresponding trans-versal
yarns.
After preforming, corresponding to the final state of the ply
Fig. 5-cand d, intra-ply yarn sliding defect occurs on the
non-sheared regionalong the radial yarns on the holder corner when
the ply exits from thedie-holder zone. Out of the defect region
(Fig. 5-d), there is no disar-rangement or misalignment between the
two yarn sets. The long-itudinal yarn dots remain aligned with
transverse yarn indicating thatno yarn sliding takes place. In the
defect region, two zones are dis-tinguished: high-density and
low-density zone of the transversal yarns.On the first one (towards
the 3D deformed zone), a gap is created be-tween the last
transverse yarn brought by the radial yarn and the nextone. About 7
successive transverse yarns along the same radial yarnscontribute
to this defect and it is expanded across 11 longitudinal yarns.The
first transversal yarn from the useful zone side shows the
maximumbending. It is therefore associated to a large gap. Below
the blank-holder, the transversal yarns accumulate creating a high
density zone asschematically represented in Fig. 3. This
accumulation of the yarnsincreases the inter-yarn contact pressure
between the two interlacedyarn sets on the crossing areas leading
to stop the yarn slippage. Out ofthe defect region, a moderate
misalignment is also observed but with alow amplitude. In the
defect zone, no out of plane displacement of yarn
Fig. 4. Preforming force for ply-0 and ply-45.
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is observed. This is even the case of yarns that bend in the ply
plane. Inthose conditions one may have expected to observe the
occurrence oftow buckles [20], but the load of the involved yarns
as well as their in-plane bending angle magnitude did not favour
the conditions of theiroccurrence. Otherwise, over the defect zones
no transversal disar-rangement of the longitudinal yarn is
observed. There is no gap be-tween the longitudinal yarns and the
dots placed on the transverseyarns remain aligned along the
longitudinal yarns axis.
5. Analysis and discussion
In this section, an analysis of the three main observations
revealedover the performed experiments is given. It has for goal to
explain whya higher preforming force for ply-45 is required in
comparison to ply-0,and also why intra-ply yarn sliding occurs only
on ply-45 when higherholder force is applied and finally why the
location of the intra-ply yarnsliding defect takes place on the
holder corner edge. Thus in this sec-tion, the effect of the
machine configuration, ply geometry and processparameters on the
preforming force and the interaction fabric/machineforces that
contribute to the appearance of the intra-ply yarn sliding
areanalysed. Also the location of the defect on the 3D shaped
preform iscorrelated to the fabric/machine interaction stress
distribution.
During the preforming process with a hemispheric-shaped
punch,the ply behaviour and particularly the deformation are
symmetricabout two orthogonal planes. The behaviour of the fabric
during thepreforming process is analysed by observing the behaviour
of radialstrips of the fabric (relative to the blank holder and die
central hole).Two strips may be distinguished on the deformed ply
in relation to thedominated deformation mechanisms: tension strip
and shear strip. Bothstrips are illustrated for ply-0 and ply-45 in
Fig. 6. The tension stripinvolves one radial yarn, which intersects
with the punch translatingaxis and it is aligned with the hole
radius of the blank-holder plate,
Fig. 6-a. The radial yarn on this strip is driven by the punch
that pulls itfrom the die-holder contact zone. During this slid an
axial tension onthe yarn due to the friction resistance on the
contact surfaces (with theother yarns and with the die-holder
system) takes place. The shearangle between the radial yarn and the
transversal yarns was measuredon the planar part of the strip (Fig.
6). The measured angles betweenthe radial and the transverse yarns
are globally equal to zero. This in-dicates that no in-plane shear
deformation takes place in this zone.Therefore, this strip is
mainly submitted to tension deformation. Theshear strip is
characterised by a trellis of crossing yarns, Fig. 6-c. Inorder to
fit the punch 3D surface shape, the crossing yarns rotate re-lative
to each other in the inter-yarn crossing area. The shear angleswere
measured on the planar part of this strip. The values vary alongthe
strip and a maximum value is observed at the holder corner
loca-tion. Therefore, the in-plane shear is considered as the
dominatingdeformation mechanism that takes place in this strip and
tension me-chanisms can be neglected. The angle between the two
strips is 45° onboth ply-0 and ply-45. The ply behaviour between
these two strips isseen as an interaction between these two
deformation types.
5.1. Analytical analysis of the radial yarn tension on the
tension strip
The preforming behaviour of the tension strip during the
preformingprocess is analysed separately in order to identify the
effect of thematerial and process parameters on this type of
deformation. Therefore,an analytical study of the fabric behaviour
during preforming with asimple curved punch surface
(hemi-cylindrical) has been conducted,Fig. 7-a. In this
configuration, the fabric strip is arranged in 0° or-ientation
relative to the axis-1, as shown in Fig. 7-a. The yarns alignedwith
the axis-1 are called longitudinal yarns. The machine
elementdimensions and boundary conditions considered previously in
thepreforming test with double curved surface punch are maintained
here.
Fig. 5. intra-ply yarn sliding on ply-45 after preforming with
0.075MPa operating pressure. Top view (a), zoomed portion (ABCD)
before preforming (b), after preforming (c) and zoomon the defect
zone after removal of the blank-holder plate (d).
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So the die (bottom plate) is fixed into position, the blank
holder force isconstant during the test and it is aligned with
axis-2. The punch isdriven from the die toward the blank-holder
with the same translationspeed. The gravity effect is ignored in
this analysis. Furthermore, themachine elements are considered as a
rigid body.
Fig. 7-b shows a side view of a half of the preforming machine,
as itis symmetric according to plane-1. In Fig. 7-b the punch is at
its topposition. The points a, b, c, d and e are marked in Fig. 7-b
on the fabricstrip in order to describe the different extents of
fabric which are incontact with the surfaces of the machine
elements. The portion a-b
Fig. 6. Top view of the ply-45 (a) and ply-0 (b) inthe deformed
state with illustration of the tensionand shear strips,
representative scheme for theshear strip (c) and tension strip
(d).
Fig. 7. Schematic diagrams representing the preforming of a
tension strip using a hemicylindrical punch (a), a side view of the
machine configuration at the top punch position (b), freebody
diagram of a portion (a–i) and (i–e) of the strip (c, d
respectively).
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= −F P Rdie2 2 (1)
To assess the internal membrane fabric tension (T) in the
long-itudinal yarn direction on the free portion b-c, an imaginary
cut is madeat a point (i) on this portion, Fig. 7-b. The membrane
fabric tension (T)in the longitudinal yarn direction represents the
sum of the longitudinalyarn tension forces across the strip width.
From the equilibrium equa-tion for the machine parts obtained from
the imaginary cut (strip por-tion a-i with punch and strip portion
i-e with dye and blank holder), therelationship between the strip
tension (T) and the external forces on themachine elements is
expressed in both direction 1 and 2 in Eqs. (2) and(3):
= ′− = − =F T T R T R T Tsin β, ; ( )holder die1 1 1 1 1 1
(2)
where T1 and F1 is the component in the direction 1 of strip
tension (T)and reaction force (F) on the punch respectively. ′T is
the strip tensionat point a in the direction 1. This force, ′T ,
involves the strip tension (T)in the free portion b-d in addition
to the friction force induced by thecontact between the fabric
strip and the punch surface, Fig. 7-c. It couldbe expressed as ′ =T
Teμα where the angle (α) represents the total angleof the
strip/punch contact area on the outside punch surface. It is
equalto the total angle of the strip/holder-corner contact surface
(c-d por-tion), Fig. 7-b. μ is the friction coefficient on this
contact surface. Thetwo forces ( ′T , F1) are considered for
equilibrium condition as theanalysis is performed for a half of the
machine for the symmetriccondition).
= = − =T F T P R T T β, ; cosdie2 2 2 2 2 (3)
where (T2) is the component of the strip tension force (T) along
the axis-2 and β is the angle between b–c portion and axis-2. It is
the comple-ment of the angle (α). At the beginning of the
preforming process wherethe fabric is flat yet, α is equal to zero.
Then it increases gradually as afunction of the displacement of the
punch. It reaches its maximumvalue at the punch top position. This
maximum value of α depends onthe machine elements geometry. So for
this configuration where aconstant holder force (P) is applied on
the upper plate, the F2,T and Rdie2forces can be expressed as a
function of the punch displacement(u punch2 ).
The strip tension (T) is the sum of the axial tension of an
individualyarn (t y) over the fabric width. The axial yarn tension
(t y) in the pre-forming process results from three deformation
mechanisms: the long-itudinal yarn stretching coupled with the
transversal yarns tension, thefabric in-plane shear and yarn
bending. Thus the fabric tension forcecan be expressed as:
∑= + +T t t t( )n
stretchingy
fabricshearingy
bendingy
(4)
where n is the number of yarns across the strip width. For the
presentconfiguration of the tension strip, the in-plane shear
deformation doesnot take place, Fig. 6. Moreover, the yarn tension
generated by thebending deformation can be ignored because of the
low carbon fibrebending rigidity. Furthermore, the transversal yarn
in the useful zone isnot subjected to axial tension.
Two regions are distinguished on the contact surface between
the
blank-holder and the fabric strip: the contact surface with the
holderflat surface (d-e portion) and the contact surface of the
holder roundedcorner (c-d portion), Fig. 7-b and d. The total
friction force ( f p1 ), alignedwith axis-1, on the fabric/flat
holder contact surface, which is exactlythe same for the fabric/die
contact surface, is the integration of thefriction shear stress (τ
p) along the strip contact length (L), which de-creases as a
function of the punch displacement, and a given strip width(w).
∫=f τ w dxpL p
1 0 (5)
The friction force ( f p1 ) is expressed as a function of the
global fabric-machine element friction coefficient (μ) and normal
contact force onthis flat area (N p2 ).
=f μ Np p1 2 (6)
From the equilibrium equation for the die plate, the component
ofreaction force in direction 2 (Rdie2 ) is equal to the normal
force (N
p2 ) on
the contact surface between the die and the portion d-e of the
strip. Sofrom Eqs. (1), (3) the normal contact force (N )p2 is
expressed as:
= = − = −N R P F P T αsinp die2 2 2 (7)
Also, the component of the reaction force in direction 1 (Rdie1
) isequal to the total tangential friction force ( f p1 ) on the
contact surfacebetween the die and the portion d-e of the
strip.
=f Rp die1 1 (8)
The total normal contact force (N r) and the total tangential
frictionforce ( f r) for the fabric strip on the holder corner are
defined as theintegration of the normal contact stress (σNr ) and
the tangential frictionshear stress (τr) along the strip curve on
the holder corner, having aradius (r) and contact angle (α), and
for the given strip width (w).
∫ ∫= =f τ wr dθ N σ w r dθ,rα r r α
Nr
0 0 (9)
Regarding the two components of the total normal and
tangentialcontact force (N r and f r) on both axis 1 and 2, Fig.
7-d, they could beexpressed as:
= =f μ N f μ N,r r r r1 2 2 1 (10)
Considering the free body diagram of the blank-holder plate and
itsequilibrium equations in both 1 and 2 directions, the following
equa-tions are obtained based on Eqs. (2, 7, 8):
− + + − = − + + =f T α N f T α f N2 cos 0, sin 0p r r r r1 1 1 2
2 (11)
Using Eqs. (1, 7, 10, and 11), the total normal force components
(Nr1andNr2 ) on the holder corner are expressed as a function of
the processparameters and the strip tension (T):
=+
− + = −Nμ
μP T cosα μsinα N Tsinα μN11
[2 ( )],r r r1 2 2 1 (12)
Here, one may notice the coupling between the strip tension and
thenormal contact force (Nr2 ) on the holder corner. As well as,
the couplingbetween the normal contact force on the fabric/flat
holder (N p2 ) and thestrip tension is noted in Eq. (7). Otherwise,
one may notice that thenormal contact force (N p2 ) is not constant
during the process even with aconstant value of P, Eq. (7). It
decreases during the preforming processwhereas the normal contact
force on the fabric/holder corner contactsurface (N r) increases.
This analysis for the relationship between theexternal forces
exerted on each machine elements and the normal andtangential
friction force on the plate and corner contact surface is
ap-plicable for any strip on the fabric during the preforming
process.
Here, the tension of a single yarn of a tension strip on a
fabric duringpreforming process is analysed. In general, the fabric
is pulled from thedie-blank holder zone when the yarn tension
overcomes the frictionforce on the contact die and blank holder
surfaces. At this condition, the
presents the strip/punch contact surface. The portion b-c
presents the free length of the fabric where the fabric is not in
contact with any machine element. At point b and c, the portion of
fabric is respectively tangent to both punch and blank holder
corner curved surfaces. The portion c-d presents the contact
surface of the fabric with the blank-holder rounded corner.
Finally, the segment d-e presents the fabric/ flat part of the
blank-holder and fabric/ die contact surfaces.
On Fig. 7, the force (F2) is the component of the preforming
force exerted by the punch in axis-2 direction. It is expressed by
the otherexternal forces on the machine elements by the holder
force (P) and thecomponent of the reaction force generated on the
die (R2die) in the axis-2 direction:
-
=t f e2y py μα1 (13)
where f py1 is the force due to the friction shear stress on the
contact areabetween this sliding yarn and the flat part of the die
and blank-holdersurface (Ap). f py1 is multiplied by 2 as the strip
is exposed to two contactsurfaces (die and holder). The area of
this surface is equal to
=A w Lp yarn . Where, w yarn is the sliding yarn width and L is
the yarnlength under the flat die and holder surface (d-e portion).
N p2 is thenormal force on the yarn/die and yarn/holder flat
contact surfaces. Thetangential friction force on a yarn ( f py1 )
is expressed as following:
= = = =f τ A N σ S f μσ A μN AS
, ,py t p p n py n p pp
1 2 1 2 (14)
where τt is the tangential friction shear stress on the
fabric/holder flatand fabric/die contact surfaces and σn is the
normal contact stress onthese two contact surfaces. S is the area
of the total fabric/die contactsurface. It is identical to the
fabric/flat holder contact area. Both of thesliding yarn area (Ap)
and the fabric contact area on the die surface (S)change during the
preforming process depending on the punch geo-metry and they can be
expressed as a function of the punch displace-ment. Thus, the
tension of one yarn (t y) on a tension strip can thereforebe
expressed as follows based on Eqs. (13) and (14):
=t μN AS
e2y pp
μα2 (15)
And based on Eq. (7):
= − = −t μ P F AS
e μ P T α AS
e2 ( ) 2 ( sin )yp
μαp
μα2 (16)
For this yarn, the evaluation of the components of the
normalcontact forces (Nry1 , Nry2 ) and tangential contact forces (
f ry1 , f
ry2 ) on the
holder corner surface during preforming can be expressed as a
functionof the process parameters and punch preforming force (F2)
based on theyarn tension defined in Eq. (15) and the relationship
between:
= =f μ N f μ N,ry ry ry ry1 2 2 1 (17)
Based on Eqs. (12, 14, 15) the contact forces on the blank
holdercorner can be expressed as a function of the process
parameters andpunch preforming force (F2):
= + − = −N f f t α N t α f2 cos , sinry py ry y ry y ry1 1 1 2 2
(18)
=−
++ −N
μ P F
μe μsinα cosα
2 ( )
1[1 ( )]ry
AS μα
12
2
p
(19)
For the present tension strip configuration on simple curved
punch,the length of all yarn across the strip width is the same
thus (Ap) area isidentic and the strip contact area on die surface
(S) is equal to:
=S nAp (20)
Where n is the number of the longitudinal yarns across the
stripwidth. Since the dominating deformation on this strip is the
tensiledeformation and regarding the identic geometry condition for
thelongitudinal yarns, the strip tension based on Eq. (15)
becomes:
=T t ny (21)
Based on Eqs. (16), (20) the yarn tension (t y) and the strip
tension(T) can be expressed as a function only of the controlled
processparameters and fabric dimensions as:
=+
tμPe
n μsinαe2
(1 2 )y
μα
μα (22)
=+
TμPeμsinαe
21 2
μα
μα (23)
To summarize the mathematical derivations presented in the
pre-vious lines, Eq. (16) indicates the friction force limit to
pull one yarn ofthe tension strip across the contact surfaces with
the machine plates(die and blank-holder). This force corresponds to
the yarn tension oncethe strip slippage initiates on these contact
surfaces. Thus this Eq. (16)permits to evaluate the tension of the
radial yarns constituting thetension strip on a fabric during
preforming process regardless the punchform. Eq. (23) presents the
total fabric tension for the simple curvedpunch with 0° orientation
of the fabric once the slippage of the fabric onthe machine plates
contact surfaces takes place. It is clear in Eqs. (16,22, 23) that
the yarn tension is proportional to the holder force (P).That
coincides with the experimental results for hemispheric pre-forming
shown in Fig. 4. Also the yarn tension depends on the
frictioncoefficient between the tools and the fabric (µ) and the
contact angle(α) at the holder corner. Regarding the friction
coefficient (µ) the fabricarchitecture and fibre surface properties
has an impact on the producedmembrane fabric tension and preforming
force. However, the me-chanical properties of the fabric have no
impact on these forces oncethe fabric, driven by the punch, starts
sliding on the machine plates.This issue is detailed in the next
section. In Eq. (16) the yarn tensiondepends also on the ratio (A
S/p ) of the contact area of the sliding yarnon the flat part of
the blank-holder (on the die) relative to the area ofcontact of the
whole preform with the die. The yarn tension (t y), thefabric strip
tension (T) and the total friction forces (f r and f p) varyduring
the preforming process because of the variation of the contactangle
as a function of the punch displacement. The evolution of
theseforces as a function of the punch displacement will be
discussed in alater Section as a function of the machine element
configuration andwill be at the basis of a discussion about the
possible occurrence of theyarn slidding defect.
5.2. Machine design: effect on the yarn tension
Two designs are reported in the literature regarding the
fixation andmobility of upper and lower plates on the preforming
machine. In otherwords, the direction of the blank holder force
relative to the punchtranslation direction. For the first
configuration, corresponding to themachine design employed for the
analysis and the experiments con-ducted previously in this study,
the lower plate is fixed while the upperplate is mobile. The blank
holder force is applied on the upper plate soit is in the opposite
direction of the punch translation [24,31], Fig. 1. Inthe second
configuration, the upper plate is fixed while lower plate ismobile
and the blank holder force is applied on lower plate in the
samedirection of the punch translation direction. This
configuration corre-sponds to the machine design constructed in
PRISME and LAMCOSlaboratories [19,33]. The aim of this section
consists in analysing theeffect of these two machine configurations
on the evolution of the yarntension by using Eq. (16). In the first
configuration, the normal contactforce (N p2 ) is not constant and
it is dependent on the punch displace-ment as shown by Eq. (7).
While in the second configuration, the holderforce is applied on
the lower plate. In this case, the normal contact force( =N Pp2 )
is constant as a function of the punch displacement. Thus,
thetension of the longitudinal yarn when the fabric sliding across
the dieand blank holder surface becomes:
=t μP AS
e2yp
μα(24)
In the tension strip configuration, the fabric tension and the
totalnormal contact force components on the holder corner once the
fabricsliding takes place becomes:
tension of one yarn (t y) at a point i on b-c portion is equal
to the friction force limit. To consider the friction on the corner
of the blank holder, the friction force may be expressed, according
to the Capstan equation [32] which describes the evolution of the
cord axial tension by the friction on a curved surface. For this
general case, the evaluation of the tension of a single yarn of the
strip is identified at first. One considers here that the yarn
displacement is in the direction of the t y force, as detailed on
Fig. 7-c:
-
=T μPe2 μα (25)
=+
− + = −Nμ
μP T cosα μsinα N Tsinα μN11
[2 ( )],r r r1 2 2 1 (26)
The evolutions of the ratio of the friction limit, corresponding
to thefabric tension (T ) once the fabric sliding takes place, and
the totalfriction force on the holder flat part and on the holder
corner part ( f p,f r) relative to the blank-holder force (P) are
plotted in Fig. 8 for the twomachine configurations. Eqs. (10, 12,
22, 25, 26) are used to plot thepreviously mentioned parameters as
a function of the punch displace-ment. Since a dry fabric is used,
one considers here only the coulombfriction for the fabric/tool
interface with a constant value equal to μ =0.3, as considered in
[24]. This is a general consideration for the fric-tion coefficient
and it permits to show the evolution of these forces foridentical
machine and fabric conditions. The total friction force on
thecontact surface of the strip/flat-part of the upper plate ( f
P/p ) in thesecond configuration (dashed blue line in Fig. 8) is
kept constant duringthe process as the normal contact force on this
surface is constant( =N Pp2 ). In the first configuration this
force (continuous blue line inFig. 8) decreases although the holder
force (operation pressure) ismaintained constant during the
process. The total friction force on thecontact surface of the
strip/corner-part of the upper plate ( f P/r ) in
bothconfigurations (black lines in Fig. 8) increases as a function
of thepunch displacement as the contact angle (α) increases.
However, in thefirst configuration (blank-holder force applied on
the upper plate), thegradient of this increase is less
important.
In order to localise the ply regions where a risk of occurrence
of theintra-ply yarn sliding defect may take place, the
distribution of thetangential shear contact stress have to be
assessed. Therefore, theevolution of the friction forces ( f p, f
r) should be associated to theevolution of the contact surface
areas. That would permit to identify therelationship between the
location of the intra-ply yarn slippage defectand the distribution
of the contact shear stress.
On the flat part of the upper and lower plates (die and
blank-holder), the contact area (Ap) decreases, as the punch goes
up, in-dependently of the machine configurations, Fig. 9. In the
second ma-chine configuration (the holder force is applied on the
lower plate), thefriction force ( f p) remains constant (the ratio
f P/p plotted in dis-continuous blue line in Fig. 8). Consequently
the shear contact stressincreases as well as the contact area
decreases. However, the increase ofthe tangential shear contact
stress is less important in the first machineconfiguration (the
holder force is applied on the upper plate) as thefriction force (
f p) decreases (the ratio f P/p plotted in blue line inFig. 8).
On the corner part of the upper plate, the contact area ( =A
Rαwr ) is
expressed as a function of the corner radius (R), the strip
width (w) andthe contact angle (α).
The corner radius is a machine geometry parameter. The effect
ofthis parameter is explored in the next section. The contact angle
(α)varies from 0°, corresponding to the initial position of the
punch, up toa maximum angle corresponding to the final position of
the punch.Hence, the area Ar increases during the process from zero
up to amaximum value at the end of the pre preforming process. The
increaseof the contact area Ar is identical for both machine
configurations. Inboth machine configurations, the total friction
force ( f r) on the cornerpart of the contact surface increases, as
a function of the punch dis-placement (Fig. 8), leading to an
increase of the shear contact stress onthis contact region.
However when comparing the two contact areas, Ar is much
smallerthan the Ap one resulting in a concentration of the shear
contact stresson this contact region. Furthermore, the distribution
of the shear stressalong this contact surface is not homogeneous.
It has a high value at thecentre of the contact surface. This
concentration of the tangential shearcontact stress on the corner
part of the upper plate could be correlatedto the position of the
occurrence of the intra-ply yarn sliding defect onthe non-sheared
zone of the preform, Fig. 5. When the tangential shearcontact
stress between the transversal yarns and the corner
surfaceovercomes the inter-yarn friction force, the yarns are stuck
on thecorner surface while the longitudinal yarns, driven by the
punch, slideacross the transversal yarns. Therefore, a gap is
observed just above thecorner surface. The accumulation of the
transversal yarns on the cornersurface increases the inter-yarns
pressure and the inter-yarns frictionuntil it overpasses again the
shear contact stress to get out of this zone.The amplitude of the
gap (number of transversal yarns stuck on thecorner) depends on the
value of the tangential shear contact stress andinter-yarns
friction contact properties. If one compares the evolution ofthe
friction force between the two machine configurations, a
lowertangential shear contact stress takes place on the contact
area in thefirst configuration (holder force applied on the upper
plate). This sug-gests that the yarn sliding defect appearance may
be delayed or mayappear with lower amplitude in that case. The
first machine config-uration also leads to a lower membrane tension
on the tension strip(Fig. 8) and as a consequence a lower
preforming force is expected, Eq.(2).
5.3. Shear strip
The shear strip consists of a trellis of crossing yarns that
shears(relative rotation between the two yarns sets at the crossing
area) as afunction of the punch displacement to fit the punch
surface shape as
Fig. 8. Friction force limit (T P/ ), the friction forceon the
holder corner ( f P/r ) and on the flat part( f P/p ) relative to
the holder force as a function ofthe punch displacement for two
machine config-urations.
-
shown in Fig. 6- c. At the beginning of the process, the
crossing yarnsshear locally in the free zone. This has for
consequence to extend thestrip length in this zone and an
additional tension in the yarns is gen-erated (denoted fabric
shearing force in Eq. (3)). This tension dependson the fabric
in-plane shear rigidity. It increases exponentially as afunction of
the shear angle increase [24] and it gets a high value whenthe
shear angle value approaches to the locking angle. The shear
de-formation propogates gradualy into the portion of the strip
placed be-tween the two machine plates when the generated shearing
effortovercomes the shear contact friction stress imposed on this
strip por-tion, Fig. 6-a and b. Therefore the shear angle value is
not uniformealong the strip length. It has a high value near the
blank hloder cornerand much lower values on the strip boarders,
Fig. 6-a and b.
5.4. Preforming process with hemispheric-shaped punch
In the frame of the preforming process with a
hemispheric-shapepunch, the analysis of the evolution of the yarn
tension as a function ofthe punch displacement in the tension strip
configuration correspondsto the evolution of the tension of the
radial yarns (the yarn that passesat the top of the hemisphere).
Moreover, for the other sliding yarns inthe useful zone the
coupling effect between the longitudinal and thetransversal yarn
tension as well as the contribution of the fabric in-plane shear
deformation will be considered.
5.4.1. Effect of ply orientationAs shown in Fig. 4, a change of
the ply orientation (ply-0 and ply-
45) with the same ply dimensions for the presented machine
geometryresults in a difference of the recorded preforming forces.
The only dif-ference between the two ply orientations is the yarn
length over the ply,as mentioned earlier in Fig. 2. On the
non-sheared zone (involving theradial yarns and neighboring yarns)
Figure 6, the radial yarn length inthe ply-45 is longer in
comparison to the ply-0 (L45=121.42mm andL0=68.8 mm). This results
in a higher (Ap/S) ratio for the ply-45 andconsequently a higher
yarn tension and preforming force on the tensionstrip according to
the Eqs. (3) and (16). The tension, the normal contactforce and the
total tangential friction force for the radial yarn in the twoply
orientations, based on the tension strip analysis, are presented
inTable 1. The radial yarn length (L) (as defined in Fig. 7) on the
diecontact surface and the total fabric/die contact surface (S)
were mea-sured on the captured photos from the formed plies. The
yarn width(particularly important for the calculation of the
sliding area) is
considered to be equal to 2.7mm. It is based on the measured
fabricproperties (3.6 yarns per cm). The force calculations were
determinedusing the Eqs. (1619) at the initial and final punch
positions(u2= 0mm and u2= 54mm, respectively), corresponding to a
contactangle for the ply on the corner part of the blank-holder
(α=0° andα=63.68° respectively). The preforming force (F) is the
mean of therecorded values for the conducted tests with an
operating pressure of0.075MPa corresponding to a blank-holder force
(P) of 952 N. One cannotice from Table 1 that the yarn length
difference induces a higher (Ap
/S) ratio for the ply-45 (about 81% larger than for ply 0) at
the finalpunch position resulting in a higher yarn tension and
higher frictionforce for the radial yarn (ty, f p, f r) of about
84% at that position for thethree parameters. The recorded maximum
preforming force on theconducted tests shows a higher value of 63%
for the ply-45 in com-parison to ply-0. On the preforming machine
used in other researchworks a disk-shaped plate with a circular
hole in its centre is sometimesused instead of the square-shaped
plate for the die and blank-holderconsidered in the present study.
With the disk-shaped die, the yarnlength on die-holder contact
surface is identical and independent of theply orientation.
5.4.2. Intra-ply yarn sliding defect in hemispheric shaped punch
preformingIntra-ply yarn sliding occurs when the friction force
between a
transversal yarn and the machine tools becomes higher than the
inter-yarn friction force at the crossing point. As a consequence,
the long-itudinal yarns driven by the punch, such as the radial
yarns, cannotbring with them the transversal yarns. Regarding the
analytical analysison the tension strip, the shear friction contact
stresses, induced duringthe preforming process, are also linked to
the membrane yarn tension.
The yarns tension is not identical over the ply surface. It
depends ontheir orientation relative to the punch and also to their
position be-tween the die and the holder plate. The radial yarns
are subjected to thehighest friction-based tension of the ply as
they are the first yarnspulled from the die and holder contact
surface. So they are driven bythe punch on its longest perimeter.
Furthermore, there is no structuralin-plane shear on the tension
strip that compensates the imposed de-formation, Fig. 6-a and b.
Otherwise, based on the analysis performedon the tension strip, the
tension of the radial yarns reaches a highervalue on the holder
corner compared to the tension on the flat holderpart. This higher
tension is associated to high normal contact forces(N ry) and
friction forces ( f ry) on the holder corner according to the
Eq.(1618). Furthermore, the ply/holder corner contact area (Ar) is
small
Fig. 9. Evolution of the contact area (A A,p r) expressedin mm2
when preforming a tension strip as a functionof the punch
displacement.
-
(Ar < Ap), Fig. 9. That results in a high contact pressure
and hightangential shear contact stress on the holder corner
contact surfaceleading to the occurrence of the intra-ply yarn
sliding defect. Regardingthe experimental tests result in Section
4.2, the intra-ply yarn slidingdefect occurs on the ply-45 in the
non-sheared zone along the radialyarns (tension strip) after the
blank holder corner where the transversalyarns are stuck on the
corner contact surface. This observation coin-cides with the
analytical analysis and the assessment of the total frictionforce
on the holder corner ( f ry) for the radial yarn given in Table 1.
Thetotal friction force at the holder corner reaches a higher value
on ply-45(87% larger than for ply-0).
It was previously indicated in Section 4.2 that the intra-ply
yarnsliding defect does not appear on the shear strip. The yarns on
this striprespond to imposed preforming displacement by an in-plane
shear de-formation to fit the punch form. This deformation is a
local structuraldeformation that does not require the translation
of the yarns along itsaxis. Thus, this deformation mechanism does
not favour the mechanismthat leads to the yarn sliding defect.
6. Solutions inhibiting the intra-ply yarn sliding defect
The proposed technical solutions in order to inhibit the
intra-plyyarn sliding defect occurrence are based on the evaluation
of the effectof the ply geometry (radial yarn length) and on the
radius (R) of thecorner of the blank-holder plate.
6.1. Ply geometry
It was noticed in the analysis of the effect of the ply
orientation onthe preforming behaviour of the ply that the
variation of the yarnlength on the contact surfaces induces a
difference in the yarn tensionand preforming force. In order to
explore into more depth the effect ofthe yarn length, two different
ply geometries for the ply-45 orientationwere considered. The new
ply geometries are considered relative to thelength of the radial
yarn across the machine plates contact surface. Theply corners are
cut into two different geometries to obtain two lengthsfor the
radial yarn (L1 and L2) as illustrated in Fig. 10. The length L2
isequal to the length of the radial yarn on the contact surface in
the ply-0configuration, ( = =L L 68.6 mm)2 0 . However, the fabric
contact area(S) for ply-45_L2 is smaller than that for ply-0 as
shown in Table 1. Thelength L1 is defined by the following
equation:
= + =L L L mm( ) 95.5112 45 0 .
Preforming tests with a hemispheric shape punch and an
operatingpressure of 0.075MPa for the holder actuators were
conducted for bothply-45_L1 and ply-45_L2. The deformed plies are
shown in Fig. 10(b andd). The preforming punch force was recorded
in both cases and plot as afunction of its displacement (Fig. 11).
It clearly appears that a shorter
radial yarn length is associated to a lower preforming force.
This ob-servation is completely consistent with Eq. (15) for a
tension strip andthe results given in Table 1. That reveals the
high impact of the yarntension caused by the friction stress on the
contact surfaces (die andblank-holder) on the preforming force. A
difference in the preformingforce is noted between the ply-0 and
ply-45_L2, Fig. 11, even if theradial yarn lengths are identical.
This difference may be attributed to ahigher fabric contact area
(S) for ply-45_L2 resulting in a higher normalcontact and friction
contact force, Eq. (15), Table 1.
During the experimental tests, the intra-ply yarn sliding defect
wasonly observed on ply-45_L1 Fig. 12-a, but with a lower amplitude
thanthe one observed for ply-45 (Fig. 5-d). Only a small gap
appears be-tween the transverse yarns on the tension strip in the
useful zone.Furthermore, this defect occurs only along the radial
yarns near theholder corner, as noticed earlier for ply-45. On the
modified ply-45_L2 aslight misalignment can be observed on the
non-sheared zone, Fig. 12-b.
As a conclusion of this section, increasing the length of the
radialyarns (or the longitudinal yarn of the non-sheared strip
between thecontact surfaces with the machine plates) has for
consequence to raisethe yarn tension resulting in higher preforming
force. It also causes therise of the normal contact force and the
frictional force on that radialyarn at the holder corner that
enhances the friction force between thetransverse yarn and the
machine tool at this zone. Consequently, thelongitudinal yarns
cannot bring the transversal yarns with them and thetransversal
yarns are locked into position on the holder corner causingthe
yarns sliding defect. On the contrary, reducing the length of
thestretched yarn by cutting the samples corners may be a solution
toprevent the occurrence of the yarn sliding defect.
6.2. Blank-holder corner radius
Eq. (16) shows the evolution of the tension of the radial yarn
as afunction of the angle (α). This angle varies during the
preformingprocess as a function of the punch displacement. However,
the angle (α)value at a given punch position also depends on the
machine elementgeometry including the holder corner radius. Fig.
7-b shows the holdercorner and the contact angle (α). In this
section, the effect of this ma-chine parameter on the preforming
force and the intra-ply yarn slidingdefect occurrence are
investigated. Increasing the corner radius reducesthe angle (α) for
the presented machine configuration. That leads to arise of the
radial yarn tension, Eq. (15). However, this has also
forconsequence to reduce the preforming force because of an
increase ofthe value of =β αcos sin in the Eq. (2). An increase of
the blank-holdercorner radius implies an increase of the contact
area ( =A Rαwr ) be-tween the ply and the holder corner. That
reduces significantly thenormal contact stress and tangential
friction contact stress on this
Table 1Radial yarn tension (ty) and frictional contact force on
the holder corner (f ry) and flat part (f py) for the ply-45 and
ply-0 and both modified plies; ply-45_L1, and ply-45_L2 at both
initialand final position of the punch.
Angle (α=0°) at u2_punch= 0
L [mm] Ap [mm2] S [mm2] Ap/S F [N] ty [N] ty/ty_ply-0 f py [N] f
ry [N]
Ply-45 121.42 655.6 55,017 0.0119 0 6.81 1.82 6,80 0Ply-45-L1
97.4 525.9 54,168 0.0097 0 5.55 1.48 5,54 0Ply-45-L2 68.65 370.7
45,892 0.0080 0 4.61 1.23 4,61 0Ply-0 68.8 371.5 56,676 0.0065 0
3.74 1 3,74 0
Angle (α=63.68°) at u2_punch= 54mm
L [mm] Ap [mm2] S [mm2] Ap/S F [N] ty [N] ty/ty_ply-0 f py [N] f
ry [N]
Ply-45 97.8 528.1 44,383 0.0119 353 5.97 1.84 4.27 1.61Ply-45-L1
71.6 386.6 42356.6 0.0091 324 4.80 1.48 3.43 1.29Ply-45-L2 43 232.2
32,704 0.0071 248 4.19 1.29 2.99 1.13Ply-0 42.35 228.7 43,490
0.0052 216 3.24 1 2.32 0.87
-
contact area (Ar). As a consequence, it reduces the risk of
occurrence ofthe intra-ply yarn sliding defect. Hemispheric
preforming tests wereconducted again for both ply-0 and ply-45 on
the same preformingmachine but with another blank holder plates
with a corner radius of6mm and 12mm. The operating pressure of the
holder actuators wasset up to 0.075MPa for all the conducted
experiments. Fig. 13 showsthe preforming force for the two ply-0
and ply-45 with the two cornerradii.
The maximum values of the angle (α) reached at the end of
thepunch course are about 64° and 59° for the 6 and 12mm corner
radiirespectively. The arc length of the ply/holder corner contact
surfacemeasures 6.69mm and 12.4 mm for the corner radii 6 and
12
respectively. That results in an increase of the contact area
(Ar) by a1.85 factor for the corner radius of 12mm compared to the
area for acorner radius of 6mm. Fig. 13 shows the recorded
preforming forces forthe two ply orientation with the two holder
corner radii. Using a highercorner radius leads to a reduction of
the preforming force for both plyorientations. However, the radial
yarn tension is slightly higher aspresented in Table 2 for the
higher radius. Here, for this new holderplate a higher preforming
force is noted in comparison to the previousresults shown in Figs.
4 and 11. That is attributed to the difference inthe surface
properties between the two blank-holder plates. Regardingthe
intra-ply yarn sliding defect on the zoomed zone illustrated inFig.
14, it occurs in the ply-45 with a die radius of 6mm. A low
Fig. 10. Modified ply-45-L1 and ply-45-L2 in theinitial state
under blank-holder before preforming(a. c) and after preforming
operation (b. d) re-spectively.
Fig. 11. Preforming force of ply-0 and ply-45 withvariation of
the radial yarn length.
-
misalignment is also observed in the ply-45 with a die radius of
12mm.No yarn sliding is observed on the ply-0 with both corner
radii. Thus thehigh increase of the corner contact area for the
higher corner radiusleads to a significant reduction of the
friction shear contact stress pre-venting (reducing) the risk of
the occurrence of the intra-ply yarnsliding at the upper plate
corner.
7. Conclusions
The behaviour of the “HexForce 48,600 U 1250” carbon wovenfabric
during the friction-based blank-holders preforming process witha
hemispheric-shaped punch was conducted with a particular
attentiongiven to the observation of the occurrence of the
intra-ply yarn slidingdefect. The experiments were performed for
two orientations of amono-ply: ply-0 and ply-45. A higher
preforming force is required toform the ply-45. Furthermore, this
higher force is associated to theoccurrence of the intra-ply yarn
sliding defect on the holder corneralong the radial yarns in the
non-sheared zone.
Fig. 12. Zoomed photo for the ply/holder corner contact zone
after preforming operation on ply-45-L1 (a) and ply-45-L2 (b).
Fig. 13. Preforming force of ply-0 and ply-45 withtwo die corner
radiuses 6 and 12mm.
Table 2Preforming force (F), radial yarn tension (ty), total
friction force and normal contact forceon the radial yarn on the
holder corner in addition to the radial yarn/holder corner area(Ar)
at the final position of the punch with two radius (R)
consideration of the holdercorner.
R= 6mm Angle (α=63.68°) at u2= 54mm
F [N] ty [N] Nry [N] f ry [N] Ar [mm2]
Ply-45 430 5.20 4.67 1.40 18Ply-0 279 2.96 2.66 0.80 18
R=12mm Angle (α=59.22°) at u2= 54mm
F [N] ty [N] Nry [N] f ry [N] Ar [mm2]
Ply-45 321.5 6.14 5.22 1.56 33.48Ply-0 192 3.27 2.78 0.83
33.48
-
Two strips from the ply were distinguished relative to the
maindeformation mechanism: tension strip and shear strip. The yarn
tensionon the tension strip was analysed analytically and related
to the frictionon both ply/die and ply/holder contact surfaces. The
analytical modelshows that the longitudinal yarn tension, once the
fabric slippage takesplace across the die and the blank holder,
depends only on the frictionproperties of the ply/tool contact
surfaces and the applied holder force.
This work also showed that the yarn tension is related to its
lengthbetween the machine plates contact surfaces. The effect of
this lengthwas investigated by testing two modified shapes for the
ply-45. It wasclear that a longer length of the radial yarn on the
contact surface in-volves higher tension within the yarns and
higher global preformingforces. This higher tension is associated
to a higher normal contact anda higher tangential friction contact
force on the ply/holder cornercontact surface. When the friction
between the transversal yarns andthe holder corner surface becomes
higher than the inter-yarns frictionat the yarn crossing area, the
radial yarns that are stretched and pulledby the punch cannot bring
the transversal yarn with them. That has forconsequence to initiate
intra-ply yarn sliding that may be considered asa preforming defect
as locally, the density of yarn may be severely re-duced and
therefore is a zone rich in resin and a potential zone ofweakness
for the composite part. Consequently, the yarn slippage
isassociated to the radial yarn tension induced by friction on the
machinetool. Thus it is important to localise the zone with the
high tangentialfriction on the ply during preforming and this work
proposed it for thestudied hemispherical shape.
This work demonstrated also that the yarn tension depends on
theangle (α) that is related to the blank-holder corner radius. Two
tests forply-0 and ply-45 were conducted with two radius values (6
and 12mm).Higher radius leads to increase the yarn tension slightly
while thepreforming force is reduced. However, as the arc length of
the ply/holder corner contact surface is longer for a larger
radius, the tangentialfriction stress is less important.
Consequently, less amplitude for theyarn slippage is observed. The
defect is therefore consequently reduced
or even suppressed.The analytical analysis of the yarn tension
for the tension strip
permits to investigate the effect of the machine condition
relative to theapplication of the holder force on the upper or
lower plate on thepredicted preforming force and yarn tension. In
the case of applying theforce on the upper plate in the opposite
direction of the punch move-ment, the yarn tension decreases during
the process. When the holderforce is applied by the lower plate,
the yarn tension increases and it isaccompanied by higher normal
contact and frictional/contact forces onthe holder corner for the
radial yarns. Consequently, the risk of oc-currence of the
intra-ply yarn sliding defect in this last case is
moresignificant.
The analysis of the evolution of process parameters and the
fabricproperties (weaving pattern, surface properties of the yarns)
should berealised in future works.
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Intra-ply yarn sliding defect in hemisphere preforming of a
woven preformIntroductionExperimental conditionsForming
machineMaterial properties and ply geometry
Definition of the intra-ply yarn sliding defectResultsPreforming
forceIntra-ply yarn sliding defect
Analysis and discussionAnalytical analysis of the radial yarn
tension on the tension stripMachine design: effect on the yarn
tensionShear stripPreforming process with hemispheric-shaped
punchEffect of ply orientationIntra-ply yarn sliding defect in
hemispheric shaped punch preforming
Solutions inhibiting the intra-ply yarn sliding defectPly
geometryBlank-holder corner radius
ConclusionsReferences